Math Common Core State Standards For Pre-K: Counting and Cardinality

(Actual standard in bold; suggestions of activities for the parents in italics)

PK.CC.1- (Count to 20.)

Your child should be able to count out loud from 0-20 effortlessly, confidently, and without hesitation!

PK.CC.2- (Represent a number of objects with a written numeral 0–5 (with 0 representing a count of no objects.)

Using different kinds of objects 0-5, your child should be able to recognize how many objects are in each group and correctly write that number. For example, if you were to show your child 3 blocks, your child would then count the number of blocks he/she sees before them and then correctly write the number “3” on a piece of paper, dry erase board, etc.

PK.CC.3A- (Understand the relationship between numbers and quantities to 10; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.)

Your child should be able to count different groups of objects, out of order, and pair them with the correct written number 1-10. For example, if you were to have stickers on different sheets of paper in this order: 7, 5, 2, 9, 6; and those numbers written on separate sheets of paper as well, then your child should be able to pick up the number “2” and pair it with the 2 stickers. Next, he/she would pick up the number “5” and match it with the 5 stickers. Then, he/she would pick up the number “6” and match it with the 6 stickers, etc.

PK.CC.3B- (Understand the relationship between numbers and quantities to 10; connect counting to cardinality. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.)

Your child should be able to recognize numbers in order. For example, if you were to count up from 0-10 saying, “1, 2, 3, 4, 5, 6, 7, 9, 10”, your child should be able to realize that you skipped over the number 8! You can also do this by showing your child a number line with certain numbers missing. You can do this by using strips of colored paper and clothespins with the numbers 0-10 written on them. You would first show your child simple number lines such as “0, 1, ___, 3, 4, 5” and say, “I wonder what number is missing?” Your child should then count out loud from 0-5, realizing that the number 2 is missing! He/she would then clip the clothespin with the number 2 written on it on the number line. You can also build your child up to more difficult number lines such as “4, 5, ___, 7, 8, ___, 10”. Not starting the number line at 0 and having more than one missing number will be more of a challenge!

PK.CC.3C- (Understand the relationship between numbers and quantities to 10; connect counting to cardinality. Understand that each successive number name refers to a quantity that is one larger.)

Your child should be able to recognize that each number on a number line 0-10 is 1 larger than the number before it. For example, have a pre-made number line 0-10 written out so you and your child can refer to it together. Next, have a pad of paper or a dry erase board and a handful of pennies handy to complete the following activity. Say, “0 + 1 = 1 and 1 comes after 0 on a number line! Can you put a finger on the number 0 and the number 1 on this number line? Great! Do you see that 1 comes after 0 because 1 is 1 bigger than 0?” Give your child 0 pennies and give yourself 1 penny and say, “Who has the greater amount of pennies, me or you?” When he/she answers that you have more pennies, re-enforce the idea that this is because 1 is 1 place greater than 0 on the number line. Continue counting out each number all the way to 10. (1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4, 4 + 1 = 5, 5 + 1 = 6, 6 + 1 = 7, 7 + 1 = 8, 8 + 1 = 9, 9 + 1 = 10.)

PK.CC.4- Count to answer “how many?” questions about as many as 10 things arranged in a line, a rectangular array, or a circle, or as many as 5 things in a scattered configuration; given a number from 1–10, count out that many objects.

Your child should be able to count objects in a group, ranging in size from 1-10. For example, have 10 different colored crayons out and ready to work with your child. Lay out 4 of these crayons and say, “How many crayons do you see?” Count with your child, “1, 2, 3, 4!” There are 4 crayons total!” (You might want to have your child touch each crayon so they know which crayons they have already counted.) Then, show your child a different grouping of crayons such as 9 and say, “How many crayons do you see?” Count with your child, “1, 2, 3, 4, 5, 6, 7, 8, 9!” There are 9 crayons total!” Keep going with this activity until your child can correctly identify each grouping of crayons 1-10.

PK.CC.5- Identify whether the number of objects in one group is more, less, greater than, fewer, and/or equal to the number of objects in another group, e.g., by using matching and counting strategies (up to 5 objects).

Your child should be able to decide what groups of objects are greater than, less than, or equal to another group of objects. For example, have a box of raisins out and dump them onto the table. Count out 3 raisins to your child and 1 raisin to yourself and say “Who has the greater amount of raisins?” Your child will say, “I do!” Say, “Very good, how did you know that?” Then have your child count each, individual raisin, “1, 2, 3! I have 3 raisins and you have 1.” Re-enforce the idea that 3 is bigger than 1. Next, count out 2 raisins to your child and 4 raisins to yourself. Say, “Who has the least or fewest amount of raisins?” Have your child count out his/her raisins and then your raisins. He/she should realize that you have more raisins since 4 is bigger than 2. Finally, count out 5 raisins to your child and 5 raisins to yourself and ask, “Who has the most raisins now?” Have your child count his/her raisins and your raisins until they realize that you each have 5. He/she should realize that you have the same number of raisins. Next, give the box of raisins to your child and let them be in charge of dealing out the raisins and asking the questions!

PK.CC.6- Identify “first” and “last” related to order or position.

Your child should be able to recognize which numbers come “first” and “last” when shown 2 numbers ranging from 1-10. For example, have a deck of cards out with the jokers, kings and queens removed. Keep the aces to represent the number 1 (you might want to right the number “1” in the middle of the ace so your child doesn’t get confused.) Next, split the deck of cards down the middle so you have 2 different piles of cards. Flip over the first card on each deck. Let’s pretend you flipped over a 5 and a 7. Ask your child, “What number comes first, 5 or 7?” Your child should say, “5 because when I count 1, 2, 3, 4, 5, I come to the number 5 before I come to the number 7.” If your child has difficulty figuring this out, suggest that they count up from 1 until they reach one of the numbers on the cards. Then, flip over the next 2 cards in the deck. Let’s pretend you flipped over an 8 and a 3. Ask your child, “What number comes last, 8 or 3?” Your child should say 8 because 8 is bigger than 3, but again, if he/she needs help, instruct them to start counting up from 1-10. When he/she reaches the number 3, say, “Oh, the last number can’t be 3 because we haven’t said the number 8 yet! Let’s keep counting to make sure, though!” Keep playing this game until your child grasps the concept. You can even keep score to make it more fun!

Operations and Algebraic Thinking

PK.OA.1- Demonstrate an understanding of addition and subtraction by using objects, fingers, and responding to practical situations (e.g., If we have 3 apples and add two more, how many apples do we have all together?).

Your child should be able to add and subtract simple numbers by using objects as counters and/or his/her fingers. For example, use pieces of fruit such as grapes to first show addition problems. Show two different groups of grapes, one group with 3 grapes and one group with 4 grapes. Have your child move the 4 grapes over to the group of 3 grapes by counting up, “4, 5, 6, 7! There are 7 grapes total!” Try a few more grape addition problems making sure that the total doesn’t go past 10. Next, try some subtraction problems. Show your child a pile of 8 grapes and say, “How many grapes would I have left if I decided to eat 3 grapes?” Count out 3 grapes and put them in a pile in front of you. Have your child count the remaining grapes out loud, “1, 2, 3, 4, 5! There would be 5 grapes left!” Say, “Good, so 8 – 3 = 5!” Continue with this activity until your child seems to be adding and subtracting with ease.

Your child should be able to extend a pattern showing 1, 2, 3, or even for shapes after the pattern has ended. For example, have out a dry erase board and different colored dry erase markers. Draw out simple shaped patterns such as a red circle, a blue star, a green triangle, a red circle, a blue star, _______. Ask your child, “What shape comes next in this pattern?” Give him/her the dry erase markers. They should pick up the green marker and draw a green triangle to the best of his/her ability. Continue different types of patterns with different shapes and colors! Your child will love drawing and learning with the dry-erase markers!

Your child should be able to look at two objects and decide which one is taller/shorter, bigger/smaller, heavier/lighter, empty/full. For example, take your child on a scavenger hung around your house! Have a “game board” made up prior to walking around that has clues on it such as “Find 2 stuffed animals in your room. Decide which stuffed animal is taller.” When you and your child go to his/her room, he/she will choose two stuffed animals that are different heights such as a yellow giraffe and a brown monkey and he/she will decide the yellow giraffe is taller. Have other clues on game board too, such as, “Go to the kitchen and find a glass that is empty and a glass that is full.” “Go to the living room and decide which object is shorter, the chair or the couch.” Etc. Have a least of at least 10 items for your child to find, compare and measure!

PK.MD.2- Sort objects into categories; count the numbers of objects in each category (limit category counts to be less than or equal to 10).

Your child should be able to sort similar objects by their attributes into categories. For example, make up a goody bag like your child would get at a birthday party. Put 10 pencils, 9 stickers, 8 crayons, 7 erasers, 6 paper clips, 5 bouncy balls, 4 pennies, 3 markers, 2 rubber bands, and 1 lollypop. Have a pre-made sheet of paper out with a picture of each object so your child knows where to place each object when they find it in the goody bag. Once they have every object on the sheet of paper, have your child count each object in each category, writing the number on the paper!

Geometry (SQUARES, CIRCLES, TRIANGLES, RECTANGLES)

PK.G.1- Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as top, bottom, up, down, in front of, behind, over, under, and next to.

Your child should be able to recognize squares, circles, triangles, and rectangles in objects that they run into in his/her everyday life and use the following terms to describe the shapes location: top, bottom, up, down, in front of, behind, over, under, next to. For example, make up a scavenger hunt sheet with pictures of a square, circle, triangle, and rectangle on top. Next, take your child outside for a walk to spot these shapes in the environment around them. For example, on your walk you may encounter a yield sign (an upside-down triangle) and say, “That shape looks like a triangle to me but something seems a little different.” Your child should then say, “Because it’s upside-down!” As you walk down the road you might point out that your neighbors door is a rectangle and is located at the top of their front steps. Soon, your child will be spotting shapes on his/her own, and when they do, document each object, shape and location on the scavenger hunt sheet you made prior to your walk! Happy shape hunting!

PK.G.2- Correctly name shapes regardless of size.

Your child should be able to identify shapes no matter what size they are. For example, cut out a variety of different sized squares, circles, triangles and rectangles (preferably small, medium and large). Mix up all the shapes on a table. Have on hand a hole punch and string and tell your child that today you are going to be making some decorations for your house but you need help picking out the correct shapes. You want all the circles to be on one line, all the triangles to be on one line, all the squares to be on one line and all the circles to be on one line. Next, have your child gather up all the shapes in 4 separate piles and sting each pile onto a piece of string. You will have a beautiful shape garland for a decoration around your house! If your child seems confused about the shapes do to their size, do an example piece of garland together saying, “Just because this square is smaller than this square doesn’t mean that it’s not a square. There are still 4 equal sides and 4 corners!”

PK.G.3- Analyze, compare, and sort two- and three-dimensional shapes and objects, in different sizes, using informal language to describe their similarities, differences, and other attributes (e.g., color, size, and shape).

Your child should be able to recognize the difference between two- dimensional and three-dimensional shapes looking at squares/cubes, rectangles/ rectangular prisms, triangle/pyramid and a circle/sphere. For example, you can play a matching game with your child in which you show them a picture of a two-dimensional shape (square, circle, rectangle, triangle) and they need to locate the three dimensional shape of that object. Have a bunch of objects in front of your child so that he/she needs to sort through the objects until they have the correct one!

Your child should be able to create squares, circles, triangles, and rectangles using objects such as modeling clay or popsicle sticks. For example, have out 4 pieces of different colored construction paper. On the top of each paper, write the name of one shape. (If this is the first time your child is “making” a shape, you might want to draw out the shape first, have he/she construct the shape to your outline, and then flip the paper over and have he/she construct the shape on their own.) Then, have your child build the 4 different shapes specified using the building materials you provided!

About the author

Heather

Originally from Saratoga Springs, NY. Heather received my Bachelor's in Elementary Education PreK-6 from SUNY Plattsburgh and my Master's in Literacy Education from The College of Saint Rose. After completing graduate school, she accepted a job teaching at Wendell Creative Arts & Science Elementary School in Wake County, North Carolina. There, she taught fifth grade for three years and third grade for a year. Heather was also involved in after school tutoring and after school care where she worked with students K-5. Heather moved back to the area to be closer to my family as it expanded after my niece and nephew were born so that she could be a proud and active Aunt. She spent the 2010-2011 school year substituting in grades K-7 in Saratoga, Schuylerville, Greenwich, Glens Falls and Ballston Spa school districts. Heather is an Education Officer at Premier Transmedia and now a writer for Plaza Familia!

I love the way the standards are broken down in this list. It looks like a lot, but it’s very clear and concise about what child should be able to do. Thanks for the info!

Felicia

I think the final standard that’s listed is a bit much for pre-K. Children need time to build their motor skills for building things. Nonetheless, very useful!

Susanna

Thanks for the useful list! I haven’t seen the core standards for pre-k yet. This a good resource to get a head start. Thanks again!

MICHELLE AUSTEN

This is a very informative and useful site. Each level is so
clearly and distinctively explained here. So precisely connecting the counting
to cardinality. This is the correct way to let them know the numbers, count
them and compare them; and thereby pushing towards algebraic thinking and later
geometry to identify shapes.

MATTHEW FITZGERALD

It’s the best way to start mathematical practices. Analysis,
comparison, identification – are the best start for the elementary level
students. I would like to suggest, that kids at this stage should be
concentrated more numbers and that’s good for them.

John Richards

Actually, it’s a developmental process towards cardinality. But
there is a big difference between a true
response and mechanically learned rule. These
are the core of the behavioral development of a child. We should be very
careful what we are delivering and how we are doing it.

Vanessa @pre-kpages.com

I would appreciate it if somewhere in your post you mentioned that these are the state standards developed by New York state and are not a part of the national Common Core State Standards. Some states are taking on the task of creating their own pre-k CCSS to align their instructions with the adoption of the CCSS in K-12, however many are not. To the best of my knowledge there will not be any CCSS developed for Pre-K on the national level because we do not have universal pre-k nationwide. Our current system of ece in the US is choppy and inadequate at best with some states offering full access to free public early childhood programs while others have nothing.